An electric power steering system is structured such that a steering operation assist force is transferred to a steering mechanism from a motor via a reduction mechanism. The reduction mechanism has a drive gear and a driven gear meshing with it. For smooth meshing, backlashes are created at where the gears mesh with each other. Upon a reverse input into the steering mechanism from the road surface, due to the backlashes, the teeth of the gears may hit each other, causing unpleasant rattling noises. In particular, in a case where the gears are made of metal instead of a synthetic resin, large rattling noises tend to occur. The patent documents 1 and 2 each disclose an electric power steering system incorporating a special elaboration for gears and their peripheries to prevent the occurrence of such large rattling noises.